Mathematical Sciences: Analytic and Algebraic Methods in Geometry and Number Theory

数学科学：几何和数论中的分析和代数方法

• 批准号: 9007857
• 负责人: Goro Shimura
• 金额: $ 25.61万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007857&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytic; Algebraic; Methods

This award supports the research in automorphic forms and representations of Professor Goro Shimura of Princeton University. Dr. Shimura's work will be concerned principally with the topics of: the periods of automorphic forms of arithmetic type; differential operators on symmetric spaces; and the special values of various zeta functions and Eisenstein series. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of modular and automorphic forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots.

该奖项支持自守形式的研究， 普林斯顿大学教授志村五郎的陈述 大学志村博士的工作将主要涉及 主题：自守形式的算术时期 型;对称空间上的微分算子;以及特殊的 各种zeta函数和爱森斯坦级数的值。 非欧平面几何始于19世纪初 世纪作为一个数学的好奇心，但在年底， 世纪，数学家们已经意识到， 基本的重要性是非欧几里德在其基本性质。 对非欧平面几何的详细研究， 上升到现代数学的几个分支，其中 模和自守形式的研究是最活跃的研究之一。 此字段主要涉及有关 整数，但在其使用的几何和分析，它 与其历史根源保持联系。